////////////////////////////////////////////////////////////////////////// // // // Pauli Spinor Algebra Package // // // // The present package implements all the basic algorithms dealing // // with Pauli spinors, which form a fundamental representation of the // // SU(2) group. The basic classes are PauliSpinor and PauliMatrix, // // which are 2-vectors and 2x2 matrices, respectively, of complex // // numbers. The generators of the group are in the standard Pauli // // sigma matrix representation. This package has particular members // // to facilitate a quantum mechanical calculation in which the Pauli // // spinor describes the spin-state of a fermion and the QM operators // // are described by Pauli matrices. Pauli matrices are also used to // // describe mixed states, ensembles that contain mixtures of particles // // described by more than one Pauli spinor. // // // // The standard Pauli matrices are generated by invoking the construc- // // to with an argument of enum type EPauliIndex. A EPauliIndex can be // // kPauliOne, kPauliSigma1, kPauliSimga2, kPauliSigma3. // // Any 2x2 matrix can be expressed as a sum over this basis. // // // // Spinors and matrices can be transformed under rotations according // // to the commutation rules for the SU(2) group. Rotations may be // // specified either by Euler angles or by a rotation axis, or by // // supplying a member of the TThreeRotation class defined in // // TFourVector.h. All angles are assumed to be in radians. // // // // This package was developed at the University of Connecticut by // // Richard T. Jones // // // //////////////////////////////////////////////////////////////////////////